De Broglie Hypothesis
The de Broglie hypothesis proposes that all matter, not just light, has an associated wavelength λ = h/p, inversely proportional to its momentum p, extending wave-particle duality from photons to every particle of matter.
Curious
By 1924, Einstein's photoelectric effect had convinced physicists that light, despite over a century of wave evidence, also behaves like a stream of particles (photons). Louis de Broglie, then a doctoral student, asked a symmetric question no one had seriously asked before: if waves can act like particles, could particles — like electrons — also act like waves?
De Broglie proposed a strikingly simple formula: every particle with momentum p has an associated wavelength λ = h/p, where h is Planck's constant. For everyday objects, moving with large momentum, this wavelength is absurdly tiny — far too small to ever observe. But for something as light as an electron, the wavelength can be large enough to produce measurable wave effects, like diffraction.
Exploring
This relation directly motivated Erwin Schrödinger's search, in late 1925, for a wave equation that matter could obey — leading within months to the Schrödinger equation, the central equation of non-relativistic quantum mechanics. De Broglie's hypothesis was thus not just a curious footnote but a direct causal step toward the full mathematical machinery of quantum theory.
Worked example: A thrown baseball (mass 0.145 kg) moving at 40 m/s has momentum p = 5.8 kg·m/s, giving a de Broglie wavelength λ = h/p = 6.626×10⁻³⁴ / 5.8 ≈ 1.14 × 10⁻³⁴ m — around 10¹⁹ times smaller than a proton, utterly unobservable and explaining why no one has ever seen a baseball diffract.
Deep Dive
De Broglie's thesis committee, including Paul Langevin, was reportedly uncertain how to evaluate such a speculative proposal and sent a copy to Einstein for assessment; Einstein's enthusiastic endorsement was decisive in the thesis being accepted. The hypothesis received direct experimental confirmation just three years later, in 1927, when Clinton Davisson and Lester Germer observed electron diffraction from a nickel crystal at Bell Labs — initially an accidental discovery during an unrelated experiment, later recognised as exactly the wave pattern de Broglie's formula predicted.
De Broglie received the 1929 Nobel Prize in Physics "for his discovery of the wave nature of electrons." The relation generalises directly to the relativistic case using relativistic momentum p = γmv, and the non-relativistic Schrödinger equation can be derived by seeking a wave equation consistent with de Broglie's relation and the classical kinetic energy expression — a derivation covered in more depth on the Schrödinger equation page.
Concept Relationship Map
Requires: wave-particle duality
Enables: Schrödinger equation, electron/neutron diffraction techniques
Commonly confused with: a literal physical vibration of the particle (rather than a wavefunction phase property)
Sources
- De Broglie, L. (1924). Doctoral thesis, Sorbonne, Paris.
- Davisson, C., Germer, L.H. (1927). "Diffraction of Electrons by a Crystal of Nickel." Physical Review, 30(6), 705–740.
- The Nobel Prize in Physics 1929 — official citation. nobelprize.org